what are the problems encountered in a chain reaction system?

Answer 1

If you are talking about Nuclear Fission, then the main problem after getting the reaction started is that too many free neutrons can become available (as each fission generates either 2 or 3 free neutrons.)

It is an exponential growth curve if some of these neutrons aren't absorbed (similar to what happened at Chrnobyl) and the reactor gets too hot and blows it lid off.

Therefore Boron or Graphite rods are introduced into the reactor core to absorb the excess neutrons - and just keep enough free neutrons flying about to keep the chain reaction going.